
Next, we estimate \(I_2\) , similar to [1]}, as below
\(I_2(\ell ) &= \left( \int _{(\mathbb {R}^N\setminus B_\rho )\cap \lbrace u(y)<0\rbrace  }\int _{B_\rho } + \int _{(\mathbb {R}^N\setminus B_\rho )\cap \lbrace u(y)\ge 0\rbrace  }\int _{B_\rho } \right) \frac{[u(x)-u(y)]^{\ell -1}w_-(x)\psi (x)^p}{|x-y|^{N+\ell s}} dxdy \\&=: I_{2,1}+ I_{2,2}.\) 
